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Search: id:A145933
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| A145933 |
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Expansion of chi(-q^6) * chi(-q^10) / (chi(-q) * chi(-q^15)) in powers of q where chi() is a Ramanujan theta function. |
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1
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| 1, 1, 1, 2, 2, 3, 3, 4, 5, 6, 7, 8, 10, 11, 14, 17, 20, 23, 27, 31, 36, 41, 48, 55, 63, 72, 82, 94, 106, 122, 137, 156, 175, 197, 222, 249, 280, 314, 352, 393, 439, 490, 546, 608, 676, 751, 834, 923, 1024, 1133, 1253, 1384, 1528, 1686, 1857, 2045, 2250, 2474, 2718, 2984
(list; graph; listen)
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OFFSET
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0,4
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FORMULA
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Expansion of eta(q^2) * eta(q^6) * eta(q^10) * eta(q^30) / (eta(q) * eta(q^12) * eta(q^15) * eta(q^20)) in powers of q.
Euler transform of a period 60 sequence.
G.f. A(x) satisfies 0 = f(A(x), A(x^2)) where f(u, v) = 2 * (1 - u)^2 * (1 - v)^2 + 2 * u*v * (u - v)^2 + u*v * (v - u^2) * (u - v^2).
G.f. is a period 1 Fourier series which satisfies f(-1 / (60 t)) = g(t) where q = exp(2 pi i t) and g() is g.f. for A058728.
G.f.: Product_{k>0} (1 + x^k) * (1 + x^(15*k)) / ((1 + x^(6*k)) * (1 + x^(10*k))).
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EXAMPLE
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1 + q + q^2 + 2*q^3 + 2*q^4 + 3*q^5 + 3*q^6 + 4*q^7 + 5*q^8 + 6*q^9 + ...
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PROGRAM
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(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A) * eta(x^6 + A) * eta(x^10 + A) * eta(x^30 + A) / (eta(x + A) * eta(x^12 + A) * eta(x^15 + A) * eta(x^20 + A)), n))}
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CROSSREFS
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A143752(n) = a(n) unless n=0. A094203(n) = a(2*n). Convolution inverse of A132968.
Sequence in context: A140952 A096911 A143752 this_sequence A120171 A145816 A027583
Adjacent sequences: A145930 A145931 A145932 this_sequence A145934 A145935 A145936
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Oct 25 2008
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